Abstract
This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.
Highlights
Advanced structural health monitoring is generally regarded as a vital technology for the generation of aeronautical and space systems [1]
square-root cubature Kalman filter (SRCKF) is used to suppress noise, and the residual innovation sequences, a priori state estimate, gain matrix and innovation covariance generated by SRCKF are employed to estimate the magnitude and location of input forces by using a nonlinear estimator
By applying residual innovation sequences, a priori state estimate, gain matrix and innovation covariance generated by SRCKF, input forces can be estimated by using a nonlinear estimator from the response values
Summary
Advanced structural health monitoring is generally regarded as a vital technology for the generation of aeronautical and space systems [1]. Kalman filter was used to suppress noise, and residual innovation sequences, a priori state estimate, and innovation covariance generated by Kalman filter were used to estimate input forces by using a least-squares method. These studies were associated with linear beam systems, and estimating dynamic input forces of nonlinear beam systems have not been studied. SRCKF is used to suppress noise, and the residual innovation sequences, a priori state estimate, gain matrix and innovation covariance generated by SRCKF are employed to estimate the magnitude and location of input forces by using a nonlinear estimator. To verify the effectiveness of this estimation method, numerical simulations of a large deflection beam and experiment of a linear beam constrained by a nonlinear spring are employed
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